Download • Reducing Fractions, Part 1

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81
Lesson 81
• Reducing Fractions, Part 1
• To find equivalent fractions, multiply by a fraction name for 1.
1 ×
__
2
3
__
3
3
= __
6
• To reduce fractions, divide by a fraction name for 1.
3 ÷ 3
1
_______
= __
6 ÷ 3
2
(3 ÷ 3 = 1)
(6 ÷ 3 = 2)
• If both terms cannot be divided by the same number, the fraction cannot be
reduced.
2
__
cannot be reduced.
5
Practice:
9
1. Reduce __
by dividing both 9 and 15 by 3.
15
2. Which of these fractions cannot be reduced?
2
A ___
10
3
B ___
10
4
C ___
10
Add, subtract, or multiply as indicated. Remember to reduce the answers.
3 × __
2 =
3. __
4
3
3 + __
3 =
4. __
8
8
2 =
4 – __
5. __
6
6
Rewrite each mixed number with a reduced fraction. Keep the whole number.
Reduce the fractions.
4 =
6. 2 __
8
Saxon Math Intermediate 5
6 =
7. 4 ___
18
6 =
8. 3 ___
15
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82
Lesson 82
• Greatest Common Factor (GCF)
• To find the greatest common factor (GCF):
1. List the factors of the smaller number in order.
2. Starting with the largest factor, cross out any factor that does not divide
evenly into the larger number.
3. Circle the first number that divides evenly into the larger number.
This is the GCF.
Example: Find the GCF of 16 and 36.
1. List the factors of 16: 1, 2, 4, 8, 16
2. Sixteen does not divide evenly into 36, so cross it out.
1, 2, 4, 8, 16
3. Eight does not divide evenly into 36, so cross it out.
1, 2, 4, 8, 16
4. Four divides evenly into 36, so circle it and stop.
1, 2, 4, 8, 16
Four is the greatest common factor of 16 and 36.
Practice:
Find the greatest common factor of each pair of numbers.
1. 8 and 12
2. 9 and 18
3. 24 and 100
4. 7 and 56
5. 18 and 44
6. 20 and 45
Reduce each fraction by dividing the terms of the fraction by their GCF.
(See problems 1–3 above.)
8
7. ___
12 =
9
8. ___ =
18
24
9. ____ =
100
90
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Saxon Math Intermediate 5
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83
Lesson 83
• Properties of Geometric Solids
• Plane figures are “flat”. They do not take up space.
• Geometric solids are shown as 3-dimensional models. They take up space.
Geometric Solids
Shape
Shape
Name
Name
Cube
Cylinder
Rectangular
prism
Sphere
Pyramid
Cone
• The flat surfaces of solids are called faces.
• Two faces meet at an edge.
• Three edges meet at a vertex.
edge
face
vertex
Practice:
Name the geometric shape of each of these real-world objects.
1. tissue box
2. juice can
3. ice cream cone
4. tennis ball
Use manipulatives for help.
5. The pyramid has how many triangular faces?
6. The pyramid has how many square faces?
7. The pyramid has how many edges?
8. The pyramid has how many vertices?
Saxon Math Intermediate 5
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84
Lesson 84
• Mean, Median, Mode, and Range
• The mean is the average (add; then divide) of the numbers.
• The median is the middle number when the set is arranged in order.
• If the list has no middle number, the median is the average of
the two middle numbers.
• The mode is the most frequent number.
• There can be more than one mode, and there can be no mode.
• The range is the difference between the greatest and the least numbers.
Practice:
Put the numbers into numerical order first.
1. 7, 8, 2, 8, 5
2. 18, 5, 10, 6, 9, 10, 19
3. 1, 12, 13, 3, 7, 8, 12
4.
Name
Age
92
Mean:
Median:
Mode:
Range:
Mean:
Median:
Mode:
Range:
Mean:
Median:
Mode:
Range:
Marcus
Sydney
Gael
Andrea
Brandon
Felina
Toby
12
10
11
12
11
16
12
Mean:
Median:
Mode:
Range:
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Saxon Math Intermediate 5
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85
Lesson 85
• Units of Capacity
• Capacity is the amount of liquid a container can hold.
• The Liquids chart shows the relationship between gallons (G), quarts (Q), pints (P),
and cups (C).
Liquids
Q Q
PP Q
PP
Q
PP
cc cc
cc cc
PP
cc cc
Equivalent Measures
U.S. Customary System
cc cc
16 oz = 1 pt
2 pt = 1 qt
4 qt = 1 gal
1 c = 8 oz
1 pt = 16 oz
1 qt = 32 oz
Metric System
1000 mL = 1 L
A liter is about 2 ounces more than a quart.
Practice:
Remember to write the units.
1. Four quarters total a dollar. How many quarts total a gallon?
2. How many cups equal one quart?
3. How many milliliters equal 4 liters?
4. A quart is two pints. A quart is how many ounces?
5. How many pints are in a gallon?
Saxon Math Intermediate 5
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Lesson 86
• Multiplying Fractions and Whole Numbers
• To multiply a fraction and a whole number:
1. Convert the whole number to a fraction. (Write the whole number over 1.)
2. Multiply the fractions.
3. Simplify the answer.
Example: What number is __25 of 8?
2 of 8
__
5
8 = ___
16 = 3 __
1
2 × __
__
5
1
5
5
Practice:
Multiply. Simplify answers when possible. Reverse the order of factors to check your
answer.
3 of 10
2. __
4
2 of 9
1. __
3
3 × ___ =
__
2 × ___ =
__
3
6. What number is __12 of 7?
6 × ___ =
__
5
1 × ___ =
__
7
7. What number is __17 of 4?
94
5
6 of 3
5. __
7
3 × ___ =
__
7
1 × ___ =
__
4
3 of 8
4. __
5
1 × ___ =
__
1 of 18
3. __
5
2
8. What number is __23 of 10?
2 × ___ =
__
3
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Saxon Math Intermediate 5
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Lesson 87
• Using Manipulatives and Sketches to Divide Fractions
• When dividing fractions, use fraction manipulatives or sketches for help.
• We can shade fraction circles to model division of fractions.
Example: How many one eighths are in one fourth?
Sketch the dividend by dividing the fraction circle
into the number of parts (fourths).
Sketch the divisor on the same fraction circle by again
dividing the fraction circle into the number of parts (eighths).
Shade the number of parts that represent the dividend
(one fourth).
Then count the number of “divisor parts” that are also shaded
(two eighths).
There are 2 “one-eighth pieces”, or two eighths, in one fourth.
We know this is right because:
2 = __
1 + __
1
1 = __
__
8
8
8
4
Practice:
Sketch and shade fraction circles to model and then answer the question.
1. How many one fourths are in one half?
2. How many one eighths are in one half?
3. How many one twelfths are in one fourth?
4. How many one sixths are in two thirds?
Find each quotient. Try answering the problems mentally.
3 =
3 ÷ __
5. __
4
4
1 =
2 ÷ __
6. __
5
5
5 ÷ __
1 =
7. __
6
6
1 =
8. 1 ÷ __
4
Saxon Math Intermediate 5
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Lesson 88
• Transformations
• Three kinds of transformations are translations (slides), reflections (flips), and
rotations (turns).
Transformations
Name
Movement
Translation
sliding a figure in one direction
without turning the figure
Reflection
reflecting a figure as in a mirror or
“flipping” a figure over a certain line
Rotation
turning a figure about a certain point
translation
reflection
rotation
• Rotations can be described by their direction and by their degree.
Clockwise is the same direction as clock hands turn.
Counterclockwise is the opposite direction as clock hands turn.
A full turn is 360˚.
A half turn is 180˚.
A quarter turn is 90˚.
90˚ clockwise
90˚ counterclockwise
Practice:
1. Sketch an uppercase letter B after a reflection in its vertical segment.
B
2. Sketch an uppercase letter B after 90º counterclockwise rotation.
B
For problems 3–5, name the transformation that could be used to position
trapezoid A on trapezoid B.
A
B
3.
A
B
4.
A
B
5.
96
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Saxon Math Intermediate 5
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89
Lesson 89
• Analyzing Prisms
• A prism is a kind of geometric solid.
• Prisms have three dimensions: length, width, and height.
• Faces of prisms are congruent if they have the same dimensions.
• Rectangular prisms have 6 rectangular faces, or sides. Triangular
prisms have 3 rectangular faces and 2 triangular bases.
• Bases or opposite faces of prisms are parallel.
• In a rectangular prism, faces that share an edge
are perpendicular.
• A cube is a rectangular prism with 6 congruent square faces.
Practice:
Name each prism below by the shape of its bases.
1.
2.
3.
4. Which faces of a triangular prism are parallel?
5. Which faces of a pyramid with a triangular base are parallel?
6. How many pairs of parallel faces does a rectangular prism have?
Refer to the geometric solids below for problems 7–8.
7. How many faces on the rectangular prism are congruent to square ABCD of
the cube below?
H
D
5
E
A
5
G
F
C
5
B
10
8. Name a face that is perpendicular to square ABCD.
Saxon Math Intermediate 5
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Name
90
Lesson 90
• Reducing Fractions, Part 2
• To reduce a fraction to lowest terms:
1.
2.
3.
4.
Cancel matching zeros (divide numerator and denominator by 10).
Find a common factor of the numerator and denominator.
Divide both by the common factor.
Repeat steps 2 and 3 until there are no common factors.
60
Example: Reduce ___
.
100
60
6
____
= ___
10
100
A comon factor of 6 and 10 is 2.
6 = ________
6 ÷ 2 = __
3
___
10
10 ÷ 2
5
• To write a percent as a reduced fraction:
1. Write the percent as a fraction.
2. Reduce the fraction.
Example: Write 84% as a reduced fraction.
84
1. 84% = ____
100
84 ÷ 4
84
21
___
2. ____ = _________
100 ÷ 4 = 25
100
Practice:
Reduce each fraction to lowest terms. Remember to find the GCF first.
3 =
1. ___
12
4 =
2. ___
20
18 =
3. ___
27
12 =
4. ___
20
15 =
5. ___
35
21 =
6. ___
24
Simplify. Reduce each answer to lowest terms.
8 + ___
2 =
7. ___
12
12
3 =
2 × __
8. __
5
4
16 =
22 – ___
9. ___
24
24
Write each percent as a reduced fraction.
10. 32% =
98
11. 50% =
12. 70% =
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
Saxon Math Intermediate 5